Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [666,2,Mod(125,666)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(666, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 11]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("666.125");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 666 = 2 \cdot 3^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 666.be (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.31803677462\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 341.1 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 666.341 |
Dual form | 666.2.be.c.125.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.258819 | + | 0.965926i | −0.183013 | + | 0.683013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | −0.448288 | − | 1.67303i | −0.200480 | − | 0.748203i | −0.990780 | − | 0.135482i | \(-0.956742\pi\) |
0.790299 | − | 0.612721i | \(-0.209925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.633975 | − | 1.09808i | 0.239620 | − | 0.415034i | −0.720985 | − | 0.692950i | \(-0.756311\pi\) |
0.960605 | + | 0.277916i | \(0.0896439\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.73205 | 0.547723 | ||||||||
\(11\) | −2.44949 | −0.738549 | −0.369274 | − | 0.929320i | \(-0.620394\pi\) | ||||
−0.369274 | + | 0.929320i | \(0.620394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.366025 | − | 0.0980762i | 0.101517 | − | 0.0272014i | −0.207703 | − | 0.978192i | \(-0.566599\pi\) |
0.309220 | + | 0.950991i | \(0.399932\pi\) | |||||||
\(14\) | 0.896575 | + | 0.896575i | 0.239620 | + | 0.239620i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −6.24384 | − | 1.67303i | −1.51435 | − | 0.405770i | −0.596476 | − | 0.802631i | \(-0.703433\pi\) |
−0.917879 | + | 0.396861i | \(0.870099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.09808 | + | 1.36603i | −1.16958 | + | 0.313388i | −0.790785 | − | 0.612093i | \(-0.790328\pi\) |
−0.378793 | + | 0.925481i | \(0.623661\pi\) | |||||||
\(20\) | −0.448288 | + | 1.67303i | −0.100240 | + | 0.374101i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.633975 | − | 2.36603i | 0.135164 | − | 0.504438i | ||||
\(23\) | −2.44949 | + | 2.44949i | −0.510754 | + | 0.510754i | −0.914757 | − | 0.404004i | \(-0.867618\pi\) |
0.404004 | + | 0.914757i | \(0.367618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.73205 | − | 1.00000i | 0.346410 | − | 0.200000i | ||||
\(26\) | 0.378937i | 0.0743157i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.09808 | + | 0.633975i | −0.207517 | + | 0.119810i | ||||
\(29\) | −6.12372 | − | 6.12372i | −1.13715 | − | 1.13715i | −0.988959 | − | 0.148188i | \(-0.952656\pi\) |
−0.148188 | − | 0.988959i | \(-0.547344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.73205 | − | 5.73205i | 1.02951 | − | 1.02951i | 0.0299555 | − | 0.999551i | \(-0.490463\pi\) |
0.999551 | − | 0.0299555i | \(-0.00953655\pi\) | |||||||
\(32\) | −0.965926 | + | 0.258819i | −0.170753 | + | 0.0457532i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.23205 | − | 5.59808i | 0.554292 | − | 0.960062i | ||||
\(35\) | −2.12132 | − | 0.568406i | −0.358569 | − | 0.0960782i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.69615 | − | 3.86603i | −0.772043 | − | 0.635571i | ||||
\(38\) | − | 5.27792i | − | 0.856191i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50000 | − | 0.866025i | −0.237171 | − | 0.136931i | ||||
\(41\) | −2.89778 | + | 5.01910i | −0.452557 | + | 0.783851i | −0.998544 | − | 0.0539421i | \(-0.982821\pi\) |
0.545987 | + | 0.837793i | \(0.316155\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.267949 | + | 0.267949i | 0.0408619 | + | 0.0408619i | 0.727242 | − | 0.686381i | \(-0.240802\pi\) |
−0.686381 | + | 0.727242i | \(0.740802\pi\) | |||||||
\(44\) | 2.12132 | + | 1.22474i | 0.319801 | + | 0.184637i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.73205 | − | 3.00000i | −0.255377 | − | 0.442326i | ||||
\(47\) | − | 4.24264i | − | 0.618853i | −0.950923 | − | 0.309426i | \(-0.899863\pi\) | ||
0.950923 | − | 0.309426i | \(-0.100137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.69615 | + | 4.66987i | 0.385165 | + | 0.667125i | ||||
\(50\) | 0.517638 | + | 1.93185i | 0.0732051 | + | 0.273205i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.366025 | − | 0.0980762i | −0.0507586 | − | 0.0136007i | ||||
\(53\) | 5.22715 | − | 3.01790i | 0.718004 | − | 0.414540i | −0.0960135 | − | 0.995380i | \(-0.530609\pi\) |
0.814018 | + | 0.580840i | \(0.197276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.09808 | + | 4.09808i | 0.148065 | + | 0.552584i | ||||
\(56\) | −0.328169 | − | 1.22474i | −0.0438535 | − | 0.163663i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.50000 | − | 4.33013i | 0.984798 | − | 0.568574i | ||||
\(59\) | 5.79555 | + | 1.55291i | 0.754517 | + | 0.202172i | 0.615521 | − | 0.788121i | \(-0.288946\pi\) |
0.138996 | + | 0.990293i | \(0.455612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.86603 | − | 10.6962i | −0.366957 | − | 1.36950i | −0.864748 | − | 0.502205i | \(-0.832522\pi\) |
0.497792 | − | 0.867297i | \(-0.334144\pi\) | |||||||
\(62\) | 4.05317 | + | 7.02030i | 0.514753 | + | 0.891579i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −0.328169 | − | 0.568406i | −0.0407044 | − | 0.0705021i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.63397 | − | 2.09808i | −0.443961 | − | 0.256321i | 0.261316 | − | 0.965253i | \(-0.415844\pi\) |
−0.705276 | + | 0.708933i | \(0.749177\pi\) | |||||||
\(68\) | 4.57081 | + | 4.57081i | 0.554292 | + | 0.554292i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.09808 | − | 1.90192i | 0.131245 | − | 0.227323i | ||||
\(71\) | −2.12132 | − | 1.22474i | −0.251754 | − | 0.145350i | 0.368813 | − | 0.929504i | \(-0.379764\pi\) |
−0.620567 | + | 0.784153i | \(0.713098\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.39230i | 0.748163i | 0.927396 | + | 0.374081i | \(0.122042\pi\) | ||||
−0.927396 | + | 0.374081i | \(0.877958\pi\) | |||||||
\(74\) | 4.94975 | − | 3.53553i | 0.575396 | − | 0.410997i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.09808 | + | 1.36603i | 0.584789 | + | 0.156694i | ||||
\(77\) | −1.55291 | + | 2.68973i | −0.176971 | + | 0.306523i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.36603 | + | 0.901924i | −0.378707 | + | 0.101474i | −0.443151 | − | 0.896447i | \(-0.646139\pi\) |
0.0644435 | + | 0.997921i | \(0.479473\pi\) | |||||||
\(80\) | 1.22474 | − | 1.22474i | 0.136931 | − | 0.136931i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.09808 | − | 4.09808i | −0.452557 | − | 0.452557i | ||||
\(83\) | 3.10583 | − | 1.79315i | 0.340909 | − | 0.196824i | −0.319765 | − | 0.947497i | \(-0.603604\pi\) |
0.660674 | + | 0.750673i | \(0.270271\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.1962i | 1.21439i | ||||||||
\(86\) | −0.328169 | + | 0.189469i | −0.0353874 | + | 0.0204309i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.73205 | + | 1.73205i | −0.184637 | + | 0.184637i | ||||
\(89\) | 1.10463 | − | 4.12252i | 0.117090 | − | 0.436986i | −0.882345 | − | 0.470604i | \(-0.844036\pi\) |
0.999435 | + | 0.0336174i | \(0.0107028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.124356 | − | 0.464102i | 0.0130360 | − | 0.0486511i | ||||
\(92\) | 3.34607 | − | 0.896575i | 0.348851 | − | 0.0934745i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.09808 | + | 1.09808i | 0.422684 | + | 0.113258i | ||||
\(95\) | 4.57081 | + | 7.91688i | 0.468955 | + | 0.812254i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.366025 | + | 0.366025i | 0.0371642 | + | 0.0371642i | 0.725445 | − | 0.688280i | \(-0.241634\pi\) |
−0.688280 | + | 0.725445i | \(0.741634\pi\) | |||||||
\(98\) | −5.20857 | + | 1.39563i | −0.526145 | + | 0.140980i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 2.20925 | 0.219829 | 0.109914 | − | 0.993941i | \(-0.464942\pi\) | ||||
0.109914 | + | 0.993941i | \(0.464942\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.73205 | + | 3.73205i | −0.367730 | + | 0.367730i | −0.866649 | − | 0.498919i | \(-0.833731\pi\) |
0.498919 | + | 0.866649i | \(0.333731\pi\) | |||||||
\(104\) | 0.189469 | − | 0.328169i | 0.0185789 | − | 0.0321797i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.56218 | + | 5.83013i | 0.151732 | + | 0.566272i | ||||
\(107\) | 9.46979 | + | 5.46739i | 0.915479 | + | 0.528552i | 0.882190 | − | 0.470894i | \(-0.156068\pi\) |
0.0332891 | + | 0.999446i | \(0.489402\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.794229 | + | 2.96410i | −0.0760733 | + | 0.283909i | −0.993475 | − | 0.114054i | \(-0.963616\pi\) |
0.917401 | + | 0.397964i | \(0.130283\pi\) | |||||||
\(110\) | −4.24264 | −0.404520 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.26795 | 0.119810 | ||||||||
\(113\) | 2.03339 | − | 7.58871i | 0.191285 | − | 0.713885i | −0.801912 | − | 0.597442i | \(-0.796184\pi\) |
0.993197 | − | 0.116444i | \(-0.0371494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.19615 | + | 3.00000i | 0.484544 | + | 0.279751i | ||||
\(116\) | 2.24144 | + | 8.36516i | 0.208112 | + | 0.776686i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.00000 | + | 5.19615i | −0.276172 | + | 0.478345i | ||||
\(119\) | −5.79555 | + | 5.79555i | −0.531278 | + | 0.531278i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 11.0735 | 1.00255 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.83013 | + | 2.09808i | −0.703166 | + | 0.188413i | ||||
\(125\) | −8.57321 | − | 8.57321i | −0.766812 | − | 0.766812i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.19615 | − | 2.07180i | −0.106141 | − | 0.183842i | 0.808063 | − | 0.589097i | \(-0.200516\pi\) |
−0.914204 | + | 0.405254i | \(0.867183\pi\) | |||||||
\(128\) | 0.965926 | + | 0.258819i | 0.0853766 | + | 0.0228766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.633975 | − | 0.169873i | 0.0556033 | − | 0.0148988i | ||||
\(131\) | −2.03339 | + | 7.58871i | −0.177658 | + | 0.663028i | 0.818426 | + | 0.574612i | \(0.194847\pi\) |
−0.996084 | + | 0.0884160i | \(0.971820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.73205 | + | 6.46410i | −0.150188 | + | 0.560509i | ||||
\(134\) | 2.96713 | − | 2.96713i | 0.256321 | − | 0.256321i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.59808 | + | 3.23205i | −0.480031 | + | 0.277146i | ||||
\(137\) | − | 16.0740i | − | 1.37329i | −0.726991 | − | 0.686647i | \(-0.759082\pi\) | ||
0.726991 | − | 0.686647i | \(-0.240918\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.339746 | − | 0.196152i | 0.0288169 | − | 0.0166374i | −0.485522 | − | 0.874224i | \(-0.661371\pi\) |
0.514339 | + | 0.857587i | \(0.328037\pi\) | |||||||
\(140\) | 1.55291 | + | 1.55291i | 0.131245 | + | 0.131245i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.73205 | − | 1.73205i | 0.145350 | − | 0.145350i | ||||
\(143\) | −0.896575 | + | 0.240237i | −0.0749754 | + | 0.0200896i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.50000 | + | 12.9904i | −0.622841 | + | 1.07879i | ||||
\(146\) | −6.17449 | − | 1.65445i | −0.511005 | − | 0.136923i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.13397 | + | 5.69615i | 0.175412 | + | 0.468221i | ||||
\(149\) | − | 15.5935i | − | 1.27747i | −0.769427 | − | 0.638735i | \(-0.779458\pi\) | ||
0.769427 | − | 0.638735i | \(-0.220542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.0000 | + | 8.66025i | 1.22068 | + | 0.704761i | 0.965064 | − | 0.262016i | \(-0.0843873\pi\) |
0.255619 | + | 0.966778i | \(0.417721\pi\) | |||||||
\(152\) | −2.63896 | + | 4.57081i | −0.214048 | + | 0.370742i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.19615 | − | 2.19615i | −0.176971 | − | 0.176971i | ||||
\(155\) | −12.1595 | − | 7.02030i | −0.976676 | − | 0.563884i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.06218 | − | 5.30385i | −0.244388 | − | 0.423293i | 0.717571 | − | 0.696485i | \(-0.245254\pi\) |
−0.961959 | + | 0.273192i | \(0.911921\pi\) | |||||||
\(158\) | − | 3.48477i | − | 0.277233i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.866025 | + | 1.50000i | 0.0684653 | + | 0.118585i | ||||
\(161\) | 1.13681 | + | 4.24264i | 0.0895933 | + | 0.334367i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.366025 | − | 0.0980762i | −0.0286693 | − | 0.00768192i | 0.244456 | − | 0.969660i | \(-0.421391\pi\) |
−0.273125 | + | 0.961978i | \(0.588057\pi\) | |||||||
\(164\) | 5.01910 | − | 2.89778i | 0.391926 | − | 0.226278i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.928203 | + | 3.46410i | 0.0720425 | + | 0.268866i | ||||
\(167\) | 6.45189 | + | 24.0788i | 0.499263 | + | 1.86327i | 0.504712 | + | 0.863288i | \(0.331599\pi\) |
−0.00544916 | + | 0.999985i | \(0.501735\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1340 | + | 6.42820i | −0.856460 | + | 0.494477i | ||||
\(170\) | −10.8147 | − | 2.89778i | −0.829446 | − | 0.222249i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0980762 | − | 0.366025i | −0.00747824 | − | 0.0279092i | ||||
\(173\) | 8.03699 | + | 13.9205i | 0.611041 | + | 1.05835i | 0.991065 | + | 0.133378i | \(0.0425824\pi\) |
−0.380024 | + | 0.924977i | \(0.624084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.53590i | − | 0.191696i | ||||||
\(176\) | −1.22474 | − | 2.12132i | −0.0923186 | − | 0.159901i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.69615 | + | 2.13397i | 0.277038 | + | 0.159948i | ||||
\(179\) | 15.8338 | + | 15.8338i | 1.18347 | + | 1.18347i | 0.978839 | + | 0.204631i | \(0.0655994\pi\) |
0.204631 | + | 0.978839i | \(0.434401\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.59808 | + | 14.8923i | −0.639090 | + | 1.10694i | 0.346543 | + | 0.938034i | \(0.387356\pi\) |
−0.985633 | + | 0.168902i | \(0.945978\pi\) | |||||||
\(182\) | 0.416102 | + | 0.240237i | 0.0308435 | + | 0.0178075i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.46410i | 0.255377i | ||||||||
\(185\) | −4.36276 | + | 9.58991i | −0.320756 | + | 0.705064i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2942 | + | 4.09808i | 1.11842 | + | 0.299681i | ||||
\(188\) | −2.12132 | + | 3.67423i | −0.154713 | + | 0.267971i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.83013 | + | 2.36603i | −0.640605 | + | 0.171650i | ||||
\(191\) | 9.14162 | − | 9.14162i | 0.661464 | − | 0.661464i | −0.294261 | − | 0.955725i | \(-0.595073\pi\) |
0.955725 | + | 0.294261i | \(0.0950734\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.90192 | − | 2.90192i | −0.208885 | − | 0.208885i | 0.594908 | − | 0.803793i | \(-0.297188\pi\) |
−0.803793 | + | 0.594908i | \(0.797188\pi\) | |||||||
\(194\) | −0.448288 | + | 0.258819i | −0.0321852 | + | 0.0185821i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 5.39230i | − | 0.385165i | ||||||
\(197\) | −9.67784 | + | 5.58750i | −0.689518 | + | 0.398093i | −0.803431 | − | 0.595397i | \(-0.796995\pi\) |
0.113914 | + | 0.993491i | \(0.463661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5885 | − | 19.5885i | 1.38859 | − | 1.38859i | 0.560297 | − | 0.828291i | \(-0.310687\pi\) |
0.828291 | − | 0.560297i | \(-0.189313\pi\) | |||||||
\(200\) | 0.517638 | − | 1.93185i | 0.0366025 | − | 0.136603i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.571797 | + | 2.13397i | −0.0402315 | + | 0.150146i | ||||
\(203\) | −10.6066 | + | 2.84203i | −0.744438 | + | 0.199471i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.69615 | + | 2.59808i | 0.677209 | + | 0.181458i | ||||
\(206\) | −2.63896 | − | 4.57081i | −0.183865 | − | 0.318463i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.267949 | + | 0.267949i | 0.0185789 | + | 0.0185789i | ||||
\(209\) | 12.4877 | − | 3.34607i | 0.863791 | − | 0.231452i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8038 | −1.22567 | −0.612834 | − | 0.790212i | \(-0.709970\pi\) | ||||
−0.612834 | + | 0.790212i | \(0.709970\pi\) | |||||||
\(212\) | −6.03579 | −0.414540 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.73205 | + | 7.73205i | −0.528552 | + | 0.528552i | ||||
\(215\) | 0.328169 | − | 0.568406i | 0.0223810 | − | 0.0387650i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.66025 | − | 9.92820i | −0.180590 | − | 0.673970i | ||||
\(218\) | −2.65754 | − | 1.53433i | −0.179991 | − | 0.103918i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.09808 | − | 4.09808i | 0.0740323 | − | 0.276292i | ||||
\(221\) | −2.44949 | −0.164771 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3923 | 1.23164 | 0.615820 | − | 0.787887i | \(-0.288825\pi\) | ||||
0.615820 | + | 0.787887i | \(0.288825\pi\) | |||||||
\(224\) | −0.328169 | + | 1.22474i | −0.0219267 | + | 0.0818317i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.80385 | + | 3.92820i | 0.452585 | + | 0.261300i | ||||
\(227\) | −5.22715 | − | 19.5080i | −0.346938 | − | 1.29479i | −0.890332 | − | 0.455312i | \(-0.849528\pi\) |
0.543394 | − | 0.839478i | \(-0.317139\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.500000 | + | 0.866025i | −0.0330409 | + | 0.0572286i | −0.882073 | − | 0.471113i | \(-0.843853\pi\) |
0.849032 | + | 0.528341i | \(0.177186\pi\) | |||||||
\(230\) | −4.24264 | + | 4.24264i | −0.279751 | + | 0.279751i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.66025 | −0.568574 | ||||||||
\(233\) | 9.38186 | 0.614626 | 0.307313 | − | 0.951609i | \(-0.400570\pi\) | ||||
0.307313 | + | 0.951609i | \(0.400570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.09808 | + | 1.90192i | −0.463027 | + | 0.124068i | ||||
\(236\) | −4.24264 | − | 4.24264i | −0.276172 | − | 0.276172i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.09808 | − | 7.09808i | −0.265639 | − | 0.460100i | ||||
\(239\) | 22.8541 | + | 6.12372i | 1.47831 | + | 0.396111i | 0.905770 | − | 0.423769i | \(-0.139293\pi\) |
0.572535 | + | 0.819880i | \(0.305960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2942 | + | 3.56218i | −0.856357 | + | 0.229460i | −0.660179 | − | 0.751108i | \(-0.729520\pi\) |
−0.196178 | + | 0.980568i | \(0.562853\pi\) | |||||||
\(242\) | 1.29410 | − | 4.82963i | 0.0831876 | − | 0.310460i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.86603 | + | 10.6962i | −0.183478 | + | 0.684751i | ||||
\(245\) | 6.60420 | − | 6.60420i | 0.421927 | − | 0.421927i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.73205 | + | 1.00000i | −0.110208 | + | 0.0636285i | ||||
\(248\) | − | 8.10634i | − | 0.514753i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.5000 | − | 6.06218i | 0.664078 | − | 0.383406i | ||||
\(251\) | 5.13922 | + | 5.13922i | 0.324384 | + | 0.324384i | 0.850446 | − | 0.526062i | \(-0.176332\pi\) |
−0.526062 | + | 0.850446i | \(0.676332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | − | 6.00000i | 0.377217 | − | 0.377217i | ||||
\(254\) | 2.31079 | − | 0.619174i | 0.144992 | − | 0.0388504i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.91567 | + | 1.58510i | 0.369010 | + | 0.0988758i | 0.438558 | − | 0.898703i | \(-0.355489\pi\) |
−0.0695487 | + | 0.997579i | \(0.522156\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.22243 | + | 2.70577i | −0.448780 | + | 0.168128i | ||||
\(260\) | 0.656339i | 0.0407044i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.80385 | − | 3.92820i | −0.420343 | − | 0.242685i | ||||
\(263\) | 2.20925 | − | 3.82654i | 0.136228 | − | 0.235954i | −0.789838 | − | 0.613316i | \(-0.789835\pi\) |
0.926066 | + | 0.377361i | \(0.123169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.39230 | − | 7.39230i | −0.454106 | − | 0.454106i | ||||
\(266\) | −5.79555 | − | 3.34607i | −0.355348 | − | 0.205160i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.09808 | + | 3.63397i | 0.128160 | + | 0.221980i | ||||
\(269\) | 4.24264i | 0.258678i | 0.991600 | + | 0.129339i | \(0.0412856\pi\) | ||||
−0.991600 | + | 0.129339i | \(0.958714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.5622 | + | 23.4904i | 0.823844 | + | 1.42694i | 0.902800 | + | 0.430061i | \(0.141508\pi\) |
−0.0789562 | + | 0.996878i | \(0.525159\pi\) | |||||||
\(272\) | −1.67303 | − | 6.24384i | −0.101443 | − | 0.378589i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.5263 | + | 4.16025i | 0.937977 | + | 0.251330i | ||||
\(275\) | −4.24264 | + | 2.44949i | −0.255841 | + | 0.147710i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.06218 | − | 26.3564i | −0.424325 | − | 1.58360i | −0.765392 | − | 0.643564i | \(-0.777455\pi\) |
0.341067 | − | 0.940039i | \(-0.389212\pi\) | |||||||
\(278\) | 0.101536 | + | 0.378937i | 0.00608972 | + | 0.0227272i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.90192 | + | 1.09808i | −0.113662 | + | 0.0656226i | ||||
\(281\) | −27.5450 | − | 7.38065i | −1.64320 | − | 0.440293i | −0.685499 | − | 0.728073i | \(-0.740416\pi\) |
−0.957696 | + | 0.287780i | \(0.907083\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.22243 | − | 19.4904i | −0.310441 | − | 1.15858i | −0.928159 | − | 0.372183i | \(-0.878609\pi\) |
0.617718 | − | 0.786400i | \(-0.288057\pi\) | |||||||
\(284\) | 1.22474 | + | 2.12132i | 0.0726752 | + | 0.125877i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.928203i | − | 0.0548858i | ||||||
\(287\) | 3.67423 | + | 6.36396i | 0.216883 | + | 0.375653i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.4641 | + | 12.3923i | 1.26259 | + | 0.728959i | ||||
\(290\) | −10.6066 | − | 10.6066i | −0.622841 | − | 0.622841i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.19615 | − | 5.53590i | 0.187041 | − | 0.323964i | ||||
\(293\) | 10.2462 | + | 5.91567i | 0.598592 | + | 0.345597i | 0.768488 | − | 0.639865i | \(-0.221010\pi\) |
−0.169895 | + | 0.985462i | \(0.554343\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 10.3923i | − | 0.605063i | ||||||
\(296\) | −6.05437 | + | 0.586988i | −0.351903 | + | 0.0341180i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.0622 | + | 4.03590i | 0.872529 | + | 0.233793i | ||||
\(299\) | −0.656339 | + | 1.13681i | −0.0379571 | + | 0.0657435i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.464102 | − | 0.124356i | 0.0267504 | − | 0.00716774i | ||||
\(302\) | −12.2474 | + | 12.2474i | −0.704761 | + | 0.704761i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.73205 | − | 3.73205i | −0.214048 | − | 0.214048i | ||||
\(305\) | −16.6102 | + | 9.58991i | −0.951098 | + | 0.549117i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 33.1244i | − | 1.89051i | −0.326337 | − | 0.945253i | \(-0.605814\pi\) | ||
0.326337 | − | 0.945253i | \(-0.394186\pi\) | |||||||
\(308\) | 2.68973 | − | 1.55291i | 0.153261 | − | 0.0884855i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.92820 | − | 9.92820i | 0.563884 | − | 0.563884i | ||||
\(311\) | −0.744272 | + | 2.77766i | −0.0422038 | + | 0.157507i | −0.983812 | − | 0.179204i | \(-0.942648\pi\) |
0.941608 | + | 0.336711i | \(0.109314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.52628 | − | 16.8923i | 0.255840 | − | 0.954810i | −0.711781 | − | 0.702402i | \(-0.752111\pi\) |
0.967621 | − | 0.252408i | \(-0.0812224\pi\) | |||||||
\(314\) | 5.91567 | − | 1.58510i | 0.333841 | − | 0.0894524i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.36603 | + | 0.901924i | 0.189354 | + | 0.0507372i | ||||
\(317\) | −7.70882 | − | 13.3521i | −0.432971 | − | 0.749927i | 0.564157 | − | 0.825668i | \(-0.309201\pi\) |
−0.997128 | + | 0.0757404i | \(0.975868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.0000 | + | 15.0000i | 0.839839 | + | 0.839839i | ||||
\(320\) | −1.67303 | + | 0.448288i | −0.0935254 | + | 0.0250600i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.39230 | −0.244774 | ||||||||
\(323\) | 34.1170 | 1.89832 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.535898 | − | 0.535898i | 0.0297263 | − | 0.0297263i | ||||
\(326\) | 0.189469 | − | 0.328169i | 0.0104937 | − | 0.0181756i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.50000 | + | 5.59808i | 0.0828236 | + | 0.309102i | ||||
\(329\) | −4.65874 | − | 2.68973i | −0.256845 | − | 0.148289i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.85641 | − | 21.8564i | 0.321897 | − | 1.20134i | −0.595497 | − | 0.803357i | \(-0.703045\pi\) |
0.917394 | − | 0.397979i | \(-0.130288\pi\) | |||||||
\(332\) | −3.58630 | −0.196824 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.9282 | −1.36401 | ||||||||
\(335\) | −1.88108 | + | 7.02030i | −0.102775 | + | 0.383560i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.2846 | − | 18.0622i | −1.70418 | − | 0.983910i | −0.941424 | − | 0.337224i | \(-0.890512\pi\) |
−0.762757 | − | 0.646685i | \(-0.776155\pi\) | |||||||
\(338\) | −3.32748 | − | 12.4183i | −0.180991 | − | 0.675468i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.59808 | − | 9.69615i | 0.303598 | − | 0.525848i | ||||
\(341\) | −14.0406 | + | 14.0406i | −0.760341 | + | 0.760341i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7128 | 0.848412 | ||||||||
\(344\) | 0.378937 | 0.0204309 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.5263 | + | 4.16025i | −0.834698 | + | 0.223657i | ||||
\(347\) | −13.3843 | − | 13.3843i | −0.718505 | − | 0.718505i | 0.249794 | − | 0.968299i | \(-0.419637\pi\) |
−0.968299 | + | 0.249794i | \(0.919637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.76795 | − | 4.79423i | −0.148165 | − | 0.256629i | 0.782384 | − | 0.622796i | \(-0.214003\pi\) |
−0.930549 | + | 0.366167i | \(0.880670\pi\) | |||||||
\(350\) | 2.44949 | + | 0.656339i | 0.130931 | + | 0.0350828i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.36603 | − | 0.633975i | 0.126110 | − | 0.0337910i | ||||
\(353\) | 6.48408 | − | 24.1989i | 0.345113 | − | 1.28798i | −0.547368 | − | 0.836892i | \(-0.684370\pi\) |
0.892480 | − | 0.451086i | \(-0.148963\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.09808 | + | 4.09808i | −0.0582798 | + | 0.217503i | ||||
\(356\) | −3.01790 | + | 3.01790i | −0.159948 | + | 0.159948i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.3923 | + | 11.1962i | −1.02492 | + | 0.591735i | ||||
\(359\) | 3.10583i | 0.163919i | 0.996636 | + | 0.0819597i | \(0.0261179\pi\) | ||||
−0.996636 | + | 0.0819597i | \(0.973882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.66987 | − | 4.42820i | 0.403678 | − | 0.233063i | ||||
\(362\) | −12.1595 | − | 12.1595i | −0.639090 | − | 0.639090i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.339746 | + | 0.339746i | −0.0178075 | + | 0.0178075i | ||||
\(365\) | 10.6945 | − | 2.86559i | 0.559778 | − | 0.149992i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.5885 | − | 25.2679i | 0.761511 | − | 1.31898i | −0.180560 | − | 0.983564i | \(-0.557791\pi\) |
0.942071 | − | 0.335412i | \(-0.108876\pi\) | |||||||
\(368\) | −3.34607 | − | 0.896575i | −0.174426 | − | 0.0467372i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.13397 | − | 6.69615i | −0.422865 | − | 0.348116i | ||||
\(371\) | − | 7.65308i | − | 0.397328i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.06218 | − | 3.50000i | −0.313888 | − | 0.181223i | 0.334777 | − | 0.942297i | \(-0.391339\pi\) |
−0.648665 | + | 0.761074i | \(0.724672\pi\) | |||||||
\(374\) | −7.91688 | + | 13.7124i | −0.409372 | + | 0.709053i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 3.00000i | −0.154713 | − | 0.154713i | ||||
\(377\) | −2.84203 | − | 1.64085i | −0.146372 | − | 0.0845079i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.56218 | − | 7.90192i | −0.234343 | − | 0.405895i | 0.724738 | − | 0.689024i | \(-0.241961\pi\) |
−0.959082 | + | 0.283130i | \(0.908627\pi\) | |||||||
\(380\) | − | 9.14162i | − | 0.468955i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.46410 | + | 11.1962i | 0.330732 | + | 0.572845i | ||||
\(383\) | 4.81105 | + | 17.9551i | 0.245833 | + | 0.917461i | 0.972963 | + | 0.230961i | \(0.0741871\pi\) |
−0.727130 | + | 0.686500i | \(0.759146\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.19615 | + | 1.39230i | 0.264820 | + | 0.0709584i | ||||
\(386\) | 3.55412 | − | 2.05197i | 0.180900 | − | 0.104443i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.133975 | − | 0.500000i | −0.00680153 | − | 0.0253837i | ||||
\(389\) | −0.536220 | − | 2.00120i | −0.0271875 | − | 0.101465i | 0.950999 | − | 0.309194i | \(-0.100059\pi\) |
−0.978186 | + | 0.207729i | \(0.933393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.3923 | − | 11.1962i | 0.980711 | − | 0.566214i | ||||
\(392\) | 5.20857 | + | 1.39563i | 0.263072 | + | 0.0704900i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.89230 | − | 10.7942i | −0.145712 | − | 0.543805i | ||||
\(395\) | 3.01790 | + | 5.22715i | 0.151847 | + | 0.263006i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7.58846i | − | 0.380854i | −0.981701 | − | 0.190427i | \(-0.939013\pi\) | ||
0.981701 | − | 0.190427i | \(-0.0609872\pi\) | |||||||
\(398\) | 13.8511 | + | 23.9909i | 0.694294 | + | 1.20255i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.73205 | + | 1.00000i | 0.0866025 | + | 0.0500000i | ||||
\(401\) | 12.0716 | + | 12.0716i | 0.602826 | + | 0.602826i | 0.941062 | − | 0.338235i | \(-0.109830\pi\) |
−0.338235 | + | 0.941062i | \(0.609830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.53590 | − | 2.66025i | 0.0765085 | − | 0.132517i | ||||
\(404\) | −1.91327 | − | 1.10463i | −0.0951887 | − | 0.0549572i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 10.9808i | − | 0.544966i | ||||||
\(407\) | 11.5032 | + | 9.46979i | 0.570191 | + | 0.469400i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.2583 | + | 7.30385i | 1.34784 | + | 0.361152i | 0.859336 | − | 0.511411i | \(-0.170877\pi\) |
0.488501 | + | 0.872563i | \(0.337544\pi\) | |||||||
\(410\) | −5.01910 | + | 8.69333i | −0.247876 | + | 0.429333i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.09808 | − | 1.36603i | 0.251164 | − | 0.0672992i | ||||
\(413\) | 5.37945 | − | 5.37945i | 0.264706 | − | 0.264706i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.39230 | − | 4.39230i | −0.215610 | − | 0.215610i | ||||
\(416\) | −0.328169 | + | 0.189469i | −0.0160898 | + | 0.00928947i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.9282i | 0.632339i | ||||||||
\(419\) | −17.5390 | + | 10.1261i | −0.856835 | + | 0.494694i | −0.862951 | − | 0.505288i | \(-0.831386\pi\) |
0.00611634 | + | 0.999981i | \(0.498053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.8301 | + | 10.8301i | −0.527828 | + | 0.527828i | −0.919924 | − | 0.392096i | \(-0.871750\pi\) |
0.392096 | + | 0.919924i | \(0.371750\pi\) | |||||||
\(422\) | 4.60797 | − | 17.1972i | 0.224313 | − | 0.837146i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.56218 | − | 5.83013i | 0.0758661 | − | 0.283136i | ||||
\(425\) | −12.4877 | + | 3.34607i | −0.605742 | + | 0.162308i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.5622 | − | 3.63397i | −0.656320 | − | 0.175860i | ||||
\(428\) | −5.46739 | − | 9.46979i | −0.264276 | − | 0.457740i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.464102 | + | 0.464102i | 0.0223810 | + | 0.0223810i | ||||
\(431\) | −19.5080 | + | 5.22715i | −0.939667 | + | 0.251783i | −0.695972 | − | 0.718069i | \(-0.745026\pi\) |
−0.243695 | + | 0.969852i | \(0.578360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.8038 | 0.903655 | 0.451828 | − | 0.892105i | \(-0.350772\pi\) | ||||
0.451828 | + | 0.892105i | \(0.350772\pi\) | |||||||
\(434\) | 10.2784 | 0.493381 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.16987 | − | 2.16987i | 0.103918 | − | 0.103918i | ||||
\(437\) | 9.14162 | − | 15.8338i | 0.437303 | − | 0.757431i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.66025 | + | 28.5885i | 0.365604 | + | 1.36445i | 0.866600 | + | 0.499003i | \(0.166300\pi\) |
−0.500996 | + | 0.865449i | \(0.667033\pi\) | |||||||
\(440\) | 3.67423 | + | 2.12132i | 0.175162 | + | 0.101130i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.633975 | − | 2.36603i | 0.0301551 | − | 0.112540i | ||||
\(443\) | −23.6627 | −1.12425 | −0.562124 | − | 0.827053i | \(-0.690016\pi\) | ||||
−0.562124 | + | 0.827053i | \(0.690016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.39230 | −0.350429 | ||||||||
\(446\) | −4.76028 | + | 17.7656i | −0.225406 | + | 0.841226i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.09808 | − | 0.633975i | −0.0518792 | − | 0.0299525i | ||||
\(449\) | −4.00240 | − | 14.9372i | −0.188885 | − | 0.704929i | −0.993765 | − | 0.111492i | \(-0.964437\pi\) |
0.804880 | − | 0.593437i | \(-0.202229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.09808 | − | 12.2942i | 0.334235 | − | 0.578913i | ||||
\(452\) | −5.55532 | + | 5.55532i | −0.261300 | + | 0.261300i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.1962 | 0.947852 | ||||||||
\(455\) | −0.832204 | −0.0390143 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.669873 | − | 0.179492i | 0.0313353 | − | 0.00839628i | −0.243117 | − | 0.969997i | \(-0.578170\pi\) |
0.274453 | + | 0.961601i | \(0.411503\pi\) | |||||||
\(458\) | −0.707107 | − | 0.707107i | −0.0330409 | − | 0.0330409i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.00000 | − | 5.19615i | −0.139876 | − | 0.242272i | ||||
\(461\) | −9.14162 | − | 2.44949i | −0.425768 | − | 0.114084i | 0.0395711 | − | 0.999217i | \(-0.487401\pi\) |
−0.465339 | + | 0.885133i | \(0.654068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.9545 | + | 10.9737i | −1.90332 | + | 0.509992i | −0.907337 | + | 0.420403i | \(0.861889\pi\) |
−0.995979 | + | 0.0895888i | \(0.971445\pi\) | |||||||
\(464\) | 2.24144 | − | 8.36516i | 0.104056 | − | 0.388343i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.42820 | + | 9.06218i | −0.112484 | + | 0.419797i | ||||
\(467\) | 3.76217 | − | 3.76217i | 0.174092 | − | 0.174092i | −0.614682 | − | 0.788775i | \(-0.710716\pi\) |
0.788775 | + | 0.614682i | \(0.210716\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.60770 | + | 2.66025i | −0.212764 | + | 0.122839i | ||||
\(470\) | − | 7.34847i | − | 0.338960i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.19615 | − | 3.00000i | 0.239172 | − | 0.138086i | ||||
\(473\) | −0.656339 | − | 0.656339i | −0.0301785 | − | 0.0301785i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.46410 | + | 7.46410i | −0.342476 | + | 0.342476i | ||||
\(476\) | 7.91688 | − | 2.12132i | 0.362869 | − | 0.0972306i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.8301 | + | 20.4904i | −0.541097 | + | 0.937208i | ||||
\(479\) | 2.68973 | + | 0.720710i | 0.122897 | + | 0.0329301i | 0.319743 | − | 0.947504i | \(-0.396403\pi\) |
−0.196846 | + | 0.980434i | \(0.563070\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.09808 | − | 0.954483i | −0.0956640 | − | 0.0435207i | ||||
\(482\) | − | 13.7632i | − | 0.626897i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.33013 | + | 2.50000i | 0.196824 | + | 0.113636i | ||||
\(485\) | 0.448288 | − | 0.776457i | 0.0203557 | − | 0.0352571i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.26795 | − | 9.26795i | −0.419971 | − | 0.419971i | 0.465223 | − | 0.885194i | \(-0.345974\pi\) |
−0.885194 | + | 0.465223i | \(0.845974\pi\) | |||||||
\(488\) | −9.58991 | − | 5.53674i | −0.434115 | − | 0.250636i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.66987 | + | 8.08846i | 0.210963 | + | 0.365399i | ||||
\(491\) | − | 22.5259i | − | 1.01658i | −0.861186 | − | 0.508289i | \(-0.830278\pi\) | ||
0.861186 | − | 0.508289i | \(-0.169722\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.9904 | + | 48.4808i | 1.26062 | + | 2.18346i | ||||
\(494\) | −0.517638 | − | 1.93185i | −0.0232896 | − | 0.0869181i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.83013 | + | 2.09808i | 0.351583 | + | 0.0942064i | ||||
\(497\) | −2.68973 | + | 1.55291i | −0.120651 | + | 0.0696577i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.366025 | + | 1.36603i | 0.0163855 | + | 0.0611517i | 0.973635 | − | 0.228113i | \(-0.0732557\pi\) |
−0.957249 | + | 0.289265i | \(0.906589\pi\) | |||||||
\(500\) | 3.13801 | + | 11.7112i | 0.140336 | + | 0.523742i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.29423 | + | 3.63397i | −0.280925 | + | 0.162192i | ||||
\(503\) | 3.67423 | + | 0.984508i | 0.163826 | + | 0.0438971i | 0.339800 | − | 0.940498i | \(-0.389641\pi\) |
−0.175974 | + | 0.984395i | \(0.556307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.990381 | − | 3.69615i | −0.0440714 | − | 0.164477i | ||||
\(506\) | 4.24264 | + | 7.34847i | 0.188608 | + | 0.326679i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.39230i | 0.106141i | ||||||||
\(509\) | −3.46618 | − | 6.00361i | −0.153636 | − | 0.266105i | 0.778926 | − | 0.627116i | \(-0.215765\pi\) |
−0.932561 | + | 0.361011i | \(0.882432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.01924 | + | 4.05256i | 0.310513 | + | 0.179275i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.06218 | + | 5.30385i | −0.135067 | + | 0.233943i | ||||
\(515\) | 7.91688 | + | 4.57081i | 0.348859 | + | 0.201414i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.3923i | 0.457053i | ||||||||
\(518\) | −0.744272 | − | 7.67664i | −0.0327014 | − | 0.337292i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.633975 | − | 0.169873i | −0.0278016 | − | 0.00744942i | ||||
\(521\) | −13.9527 | + | 24.1667i | −0.611277 | + | 1.05876i | 0.379748 | + | 0.925090i | \(0.376011\pi\) |
−0.991025 | + | 0.133674i | \(0.957323\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.5885 | + | 8.46410i | −1.38127 | + | 0.370109i | −0.871581 | − | 0.490251i | \(-0.836905\pi\) |
−0.509686 | + | 0.860361i | \(0.670238\pi\) | |||||||
\(524\) | 5.55532 | − | 5.55532i | 0.242685 | − | 0.242685i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.12436 | + | 3.12436i | 0.136228 | + | 0.136228i | ||||
\(527\) | −45.3799 | + | 26.2001i | −1.97678 | + | 1.14129i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000i | 0.478261i | ||||||||
\(530\) | 9.05369 | − | 5.22715i | 0.393267 | − | 0.227053i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.73205 | − | 4.73205i | 0.205160 | − | 0.205160i | ||||
\(533\) | −0.568406 | + | 2.12132i | −0.0246204 | + | 0.0918846i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.90192 | − | 18.2942i | 0.211929 | − | 0.790928i | ||||
\(536\) | −4.05317 | + | 1.08604i | −0.175070 | + | 0.0469100i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.09808 | − | 1.09808i | −0.176681 | − | 0.0473414i | ||||
\(539\) | −6.60420 | − | 11.4388i | −0.284463 | − | 0.492704i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.4186 | + | 19.4186i | 0.834870 | + | 0.834870i | 0.988178 | − | 0.153308i | \(-0.0489927\pi\) |
−0.153308 | + | 0.988178i | \(0.548993\pi\) | |||||||
\(542\) | −26.2001 | + | 7.02030i | −1.12539 | + | 0.301548i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.46410 | 0.277146 | ||||||||
\(545\) | 5.31508 | 0.227673 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.3205 | + | 28.3205i | −1.21090 | + | 1.21090i | −0.240166 | + | 0.970732i | \(0.577202\pi\) |
−0.970732 | + | 0.240166i | \(0.922798\pi\) | |||||||
\(548\) | −8.03699 | + | 13.9205i | −0.343323 | + | 0.594653i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.26795 | − | 4.73205i | −0.0540655 | − | 0.201775i | ||||
\(551\) | 39.5844 | + | 22.8541i | 1.68635 | + | 0.973615i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.14359 | + | 4.26795i | −0.0486305 | + | 0.181492i | ||||
\(554\) | 27.2862 | 1.15928 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.392305 | −0.0166374 | ||||||||
\(557\) | 4.53862 | − | 16.9384i | 0.192308 | − | 0.717702i | −0.800640 | − | 0.599146i | \(-0.795507\pi\) |
0.992947 | − | 0.118556i | \(-0.0378265\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.124356 | + | 0.0717968i | 0.00525968 | + | 0.00303668i | ||||
\(560\) | −0.568406 | − | 2.12132i | −0.0240195 | − | 0.0896421i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.2583 | − | 24.6962i | 0.601451 | − | 1.04174i | ||||
\(563\) | 28.7375 | − | 28.7375i | 1.21114 | − | 1.21114i | 0.240492 | − | 0.970651i | \(-0.422691\pi\) |
0.970651 | − | 0.240492i | \(-0.0773087\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.6077 | −0.572480 | ||||||||
\(566\) | 20.1779 | 0.848142 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.36603 | + | 0.633975i | −0.0992762 | + | 0.0266010i | ||||
\(569\) | −17.7148 | − | 17.7148i | −0.742644 | − | 0.742644i | 0.230442 | − | 0.973086i | \(-0.425983\pi\) |
−0.973086 | + | 0.230442i | \(0.925983\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9282 | + | 22.3923i | 0.541028 | + | 0.937089i | 0.998845 | + | 0.0480423i | \(0.0152982\pi\) |
−0.457817 | + | 0.889047i | \(0.651368\pi\) | |||||||
\(572\) | 0.896575 | + | 0.240237i | 0.0374877 | + | 0.0100448i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.09808 | + | 1.90192i | −0.296268 | + | 0.0793848i | ||||
\(575\) | −1.79315 | + | 6.69213i | −0.0747796 | + | 0.279081i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.70577 | + | 13.8301i | −0.154273 | + | 0.575756i | 0.844893 | + | 0.534935i | \(0.179664\pi\) |
−0.999166 | + | 0.0408207i | \(0.987003\pi\) | |||||||
\(578\) | −17.5254 | + | 17.5254i | −0.728959 | + | 0.728959i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.9904 | − | 7.50000i | 0.539396 | − | 0.311421i | ||||
\(581\) | − | 4.54725i | − | 0.188652i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.8038 | + | 7.39230i | −0.530281 | + | 0.306158i | ||||
\(584\) | 4.52004 | + | 4.52004i | 0.187041 | + | 0.187041i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.36603 | + | 8.36603i | −0.345597 | + | 0.345597i | ||||
\(587\) | 12.4877 | − | 3.34607i | 0.515422 | − | 0.138107i | 0.00827376 | − | 0.999966i | \(-0.497366\pi\) |
0.507148 | + | 0.861859i | \(0.330700\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.3923 | + | 37.0526i | −0.881455 | + | 1.52672i | ||||
\(590\) | 10.0382 | + | 2.68973i | 0.413266 | + | 0.110734i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | − | 6.00000i | 0.0410997 | − | 0.246598i | ||||
\(593\) | − | 21.1488i | − | 0.868478i | −0.900798 | − | 0.434239i | \(-0.857017\pi\) | ||
0.900798 | − | 0.434239i | \(-0.142983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.2942 | + | 7.09808i | 0.504014 | + | 0.290993i | ||||
\(596\) | −7.79676 | + | 13.5044i | −0.319368 | + | 0.553161i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.928203 | − | 0.928203i | −0.0379571 | − | 0.0379571i | ||||
\(599\) | −14.4331 | − | 8.33298i | −0.589722 | − | 0.340476i | 0.175266 | − | 0.984521i | \(-0.443922\pi\) |
−0.764988 | + | 0.644045i | \(0.777255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.2321 | − | 21.1865i | −0.498956 | − | 0.864217i | 0.501044 | − | 0.865422i | \(-0.332950\pi\) |
−0.999999 | + | 0.00120537i | \(0.999616\pi\) | |||||||
\(602\) | 0.480473i | 0.0195826i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.66025 | − | 15.0000i | −0.352381 | − | 0.610341i | ||||
\(605\) | 2.24144 | + | 8.36516i | 0.0911274 | + | 0.340092i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.4904 | − | 10.0455i | −1.52169 | − | 0.407735i | −0.601391 | − | 0.798955i | \(-0.705386\pi\) |
−0.920297 | + | 0.391220i | \(0.872053\pi\) | |||||||
\(608\) | 4.57081 | − | 2.63896i | 0.185371 | − | 0.107024i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.96410 | − | 18.5263i | −0.200991 | − | 0.750107i | ||||
\(611\) | −0.416102 | − | 1.55291i | −0.0168337 | − | 0.0628242i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.0885 | − | 15.0622i | 1.05370 | − | 0.608356i | 0.130019 | − | 0.991511i | \(-0.458496\pi\) |
0.923684 | + | 0.383156i | \(0.125163\pi\) | |||||||
\(614\) | 31.9957 | + | 8.57321i | 1.29124 | + | 0.345987i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.803848 | + | 3.00000i | 0.0323879 | + | 0.120873i | ||||
\(617\) | 17.4746 | + | 30.2669i | 0.703501 | + | 1.21850i | 0.967230 | + | 0.253902i | \(0.0817142\pi\) |
−0.263729 | + | 0.964597i | \(0.584952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.1962i | 1.77639i | 0.459463 | + | 0.888197i | \(0.348042\pi\) | ||||
−0.459463 | + | 0.888197i | \(0.651958\pi\) | |||||||
\(620\) | 7.02030 | + | 12.1595i | 0.281942 | + | 0.488338i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.49038 | − | 1.43782i | −0.0998552 | − | 0.0576514i | ||||
\(623\) | −3.82654 | − | 3.82654i | −0.153307 | − | 0.153307i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 15.1452 | + | 8.74410i | 0.605325 | + | 0.349485i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.12436i | 0.244388i | ||||||||
\(629\) | 22.8541 | + | 31.9957i | 0.911251 | + | 1.27575i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.6603 | + | 2.85641i | 0.424378 | + | 0.113712i | 0.464686 | − | 0.885476i | \(-0.346167\pi\) |
−0.0403079 | + | 0.999187i | \(0.512834\pi\) | |||||||
\(632\) | −1.74238 | + | 3.01790i | −0.0693083 | + | 0.120045i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.8923 | − | 3.99038i | 0.591449 | − | 0.158478i | ||||
\(635\) | −2.92996 | + | 2.92996i | −0.116272 | + | 0.116272i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.44486 | + | 1.44486i | 0.0572476 | + | 0.0572476i | ||||
\(638\) | −18.3712 | + | 10.6066i | −0.727322 | + | 0.419919i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 1.73205i | − | 0.0684653i | ||||||
\(641\) | 42.3299 | − | 24.4392i | 1.67193 | − | 0.965288i | 0.705371 | − | 0.708838i | \(-0.250780\pi\) |
0.966557 | − | 0.256450i | \(-0.0825530\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.3397 | + | 13.3397i | −0.526068 | + | 0.526068i | −0.919398 | − | 0.393329i | \(-0.871323\pi\) |
0.393329 | + | 0.919398i | \(0.371323\pi\) | |||||||
\(644\) | 1.13681 | − | 4.24264i | 0.0447967 | − | 0.167183i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.83013 | + | 32.9545i | −0.347417 | + | 1.29658i | ||||
\(647\) | −26.8565 | + | 7.19617i | −1.05584 | + | 0.282910i | −0.744662 | − | 0.667442i | \(-0.767389\pi\) |
−0.311175 | + | 0.950353i | \(0.600722\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.1962 | − | 3.80385i | −0.557248 | − | 0.149314i | ||||
\(650\) | 0.378937 | + | 0.656339i | 0.0148631 | + | 0.0257437i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.267949 | + | 0.267949i | 0.0104937 | + | 0.0104937i | ||||
\(653\) | −13.5923 | + | 3.64205i | −0.531908 | + | 0.142524i | −0.514769 | − | 0.857329i | \(-0.672122\pi\) |
−0.0171389 | + | 0.999853i | \(0.505456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.6077 | 0.531697 | ||||||||
\(656\) | −5.79555 | −0.226278 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.80385 | − | 3.80385i | 0.148289 | − | 0.148289i | ||||
\(659\) | 17.8671 | − | 30.9468i | 0.696005 | − | 1.20552i | −0.273836 | − | 0.961776i | \(-0.588293\pi\) |
0.969841 | − | 0.243739i | \(-0.0783742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.55256 | − | 28.1865i | −0.293760 | − | 1.09633i | −0.942197 | − | 0.335060i | \(-0.891243\pi\) |
0.648436 | − | 0.761269i | \(-0.275423\pi\) | |||||||
\(662\) | 19.5959 | + | 11.3137i | 0.761617 | + | 0.439720i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.928203 | − | 3.46410i | 0.0360213 | − | 0.134433i | ||||
\(665\) | 11.5911 | 0.449484 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.0000 | 1.16160 | ||||||||
\(668\) | 6.45189 | − | 24.0788i | 0.249631 | − | 0.931637i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.29423 | − | 3.63397i | −0.243167 | − | 0.140393i | ||||
\(671\) | 7.02030 | + | 26.2001i | 0.271016 | + | 1.01144i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6603 | − | 20.1962i | 0.449470 | − | 0.778504i | −0.548882 | − | 0.835900i | \(-0.684946\pi\) |
0.998352 | + | 0.0573955i | \(0.0182796\pi\) | |||||||
\(674\) | 25.5438 | − | 25.5438i | 0.983910 | − | 0.983910i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.8564 | 0.494477 | ||||||||
\(677\) | −20.3166 | −0.780831 | −0.390416 | − | 0.920639i | \(-0.627669\pi\) | ||||
−0.390416 | + | 0.920639i | \(0.627669\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.633975 | − | 0.169873i | 0.0243297 | − | 0.00651913i | ||||
\(680\) | 7.91688 | + | 7.91688i | 0.303598 | + | 0.303598i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.92820 | − | 17.1962i | −0.380171 | − | 0.658475i | ||||
\(683\) | 14.3688 | + | 3.85010i | 0.549806 | + | 0.147320i | 0.523019 | − | 0.852321i | \(-0.324806\pi\) |
0.0267869 | + | 0.999641i | \(0.491472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.8923 | + | 7.20577i | −1.02750 | + | 0.275318i | ||||
\(686\) | −4.06678 | + | 15.1774i | −0.155270 | + | 0.579476i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0980762 | + | 0.366025i | −0.00373912 | + | 0.0139546i | ||||
\(689\) | 1.61729 | − | 1.61729i | 0.0616137 | − | 0.0616137i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.5622 | + | 11.2942i | −0.744180 | + | 0.429653i | −0.823587 | − | 0.567190i | \(-0.808031\pi\) |
0.0794069 | + | 0.996842i | \(0.474697\pi\) | |||||||
\(692\) | − | 16.0740i | − | 0.611041i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.3923 | − | 9.46410i | 0.622243 | − | 0.359252i | ||||
\(695\) | −0.480473 | − | 0.480473i | −0.0182254 | − | 0.0182254i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.4904 | − | 26.4904i | 1.00339 | − | 1.00339i | ||||
\(698\) | 5.34727 | − | 1.43280i | 0.202397 | − | 0.0542321i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.26795 | + | 2.19615i | −0.0479240 | + | 0.0830068i | ||||
\(701\) | −15.8338 | − | 4.24264i | −0.598033 | − | 0.160242i | −0.0529108 | − | 0.998599i | \(-0.516850\pi\) |
−0.545122 | + | 0.838357i | \(0.683517\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.2224 | + | 13.2942i | 1.10214 | + | 0.501401i | ||||
\(704\) | 2.44949i | 0.0923186i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.6962 | + | 12.5263i | 0.816545 | + | 0.471433i | ||||
\(707\) | 1.40061 | − | 2.42593i | 0.0526754 | − | 0.0912364i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.9282 | − | 25.9282i | −0.973754 | − | 0.973754i | 0.0259102 | − | 0.999664i | \(-0.491752\pi\) |
−0.999664 | + | 0.0259102i | \(0.991752\pi\) | |||||||
\(710\) | −3.67423 | − | 2.12132i | −0.137892 | − | 0.0796117i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.13397 | − | 3.69615i | −0.0799741 | − | 0.138519i | ||||
\(713\) | 28.0812i | 1.05165i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.803848 | + | 1.39230i | 0.0300622 | + | 0.0520692i | ||||
\(716\) | −5.79555 | − | 21.6293i | −0.216590 | − | 0.808325i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.00000 | − | 0.803848i | −0.111959 | − | 0.0299993i | ||||
\(719\) | −10.8704 | + | 6.27603i | −0.405398 | + | 0.234056i | −0.688810 | − | 0.724942i | \(-0.741867\pi\) |
0.283413 | + | 0.958998i | \(0.408533\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.73205 | + | 6.46410i | 0.0645049 | + | 0.240736i | ||||
\(722\) | 2.29221 | + | 8.55463i | 0.0853071 | + | 0.318370i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.8923 | − | 8.59808i | 0.553468 | − | 0.319545i | ||||
\(725\) | −16.7303 | − | 4.48288i | −0.621349 | − | 0.166490i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.4641 | − | 42.7846i | −0.425180 | − | 1.58679i | −0.763530 | − | 0.645773i | \(-0.776535\pi\) |
0.338350 | − | 0.941020i | \(-0.390131\pi\) | |||||||
\(728\) | −0.240237 | − | 0.416102i | −0.00890376 | − | 0.0154218i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.0718i | 0.409786i | ||||||||
\(731\) | −1.22474 | − | 2.12132i | −0.0452988 | − | 0.0784599i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.00000 | + | 3.46410i | 0.221615 | + | 0.127950i | 0.606698 | − | 0.794933i | \(-0.292494\pi\) |
−0.385083 | + | 0.922882i | \(0.625827\pi\) | |||||||
\(734\) | 20.6312 | + | 20.6312i | 0.761511 | + | 0.761511i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.73205 | − | 3.00000i | 0.0638442 | − | 0.110581i | ||||
\(737\) | 8.90138 | + | 5.13922i | 0.327887 | + | 0.189305i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.3923i | 1.04443i | 0.852815 | + | 0.522214i | \(0.174894\pi\) | ||||
−0.852815 | + | 0.522214i | \(0.825106\pi\) | |||||||
\(740\) | 8.57321 | − | 6.12372i | 0.315158 | − | 0.225113i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.39230 | + | 1.98076i | 0.271380 | + | 0.0727161i | ||||
\(743\) | −2.12132 | + | 3.67423i | −0.0778237 | + | 0.134795i | −0.902311 | − | 0.431086i | \(-0.858130\pi\) |
0.824487 | + | 0.565881i | \(0.191464\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.0885 | + | 6.99038i | −0.955807 | + | 0.256108i | ||||
\(746\) | 4.94975 | − | 4.94975i | 0.181223 | − | 0.181223i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.1962 | − | 11.1962i | −0.409372 | − | 0.409372i | ||||
\(749\) | 12.0072 | − | 6.93237i | 0.438734 | − | 0.253303i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.5885i | 1.84600i | 0.384801 | + | 0.923000i | \(0.374270\pi\) | ||||
−0.384801 | + | 0.923000i | \(0.625730\pi\) | |||||||
\(752\) | 3.67423 | − | 2.12132i | 0.133986 | − | 0.0773566i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.32051 | − | 2.32051i | 0.0845079 | − | 0.0845079i | ||||
\(755\) | 7.76457 | − | 28.9778i | 0.282582 | − | 1.05461i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.91858 | − | 37.0167i | 0.360497 | − | 1.34539i | −0.512927 | − | 0.858432i | \(-0.671439\pi\) |
0.873424 | − | 0.486961i | \(-0.161895\pi\) | |||||||
\(758\) | 8.81345 | − | 2.36156i | 0.320119 | − | 0.0857756i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.83013 | + | 2.36603i | 0.320302 | + | 0.0858248i | ||||
\(761\) | 0.776457 | + | 1.34486i | 0.0281465 | + | 0.0487513i | 0.879756 | − | 0.475426i | \(-0.157706\pi\) |
−0.851609 | + | 0.524178i | \(0.824373\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.75129 | + | 2.75129i | 0.0996033 | + | 0.0996033i | ||||
\(764\) | −12.4877 | + | 3.34607i | −0.451789 | + | 0.121056i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.5885 | −0.671628 | ||||||||
\(767\) | 2.27362 | 0.0820958 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.1962 | + | 27.1962i | −0.980718 | + | 0.980718i | −0.999818 | − | 0.0190993i | \(-0.993920\pi\) |
0.0190993 | + | 0.999818i | \(0.493920\pi\) | |||||||
\(770\) | −2.68973 | + | 4.65874i | −0.0969310 | + | 0.167889i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.06218 | + | 3.96410i | 0.0382286 | + | 0.142671i | ||||
\(773\) | 14.0728 | + | 8.12493i | 0.506163 | + | 0.292233i | 0.731255 | − | 0.682104i | \(-0.238935\pi\) |
−0.225092 | + | 0.974337i | \(0.572268\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.19615 | − | 15.6603i | 0.150730 | − | 0.562533i | ||||
\(776\) | 0.517638 | 0.0185821 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.07180 | 0.0742775 | ||||||||
\(779\) | 7.91688 | − | 29.5462i | 0.283651 | − | 1.05860i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.19615 | + | 3.00000i | 0.185933 | + | 0.107348i | ||||
\(782\) | 5.79555 | + | 21.6293i | 0.207249 | + | 0.773462i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.69615 | + | 4.66987i | −0.0962912 | + | 0.166781i | ||||
\(785\) | −7.50077 | + | 7.50077i | −0.267714 | + | 0.267714i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.00000 | 0.285169 | 0.142585 | − | 0.989783i | \(-0.454459\pi\) | ||||
0.142585 | + | 0.989783i | \(0.454459\pi\) | |||||||
\(788\) | 11.1750 | 0.398093 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.83013 | + | 1.56218i | −0.207427 | + | 0.0555798i | ||||
\(791\) | −7.04386 | − | 7.04386i | −0.250451 | − | 0.250451i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.09808 | − | 3.63397i | −0.0745049 | − | 0.129046i | ||||
\(794\) | 7.32989 | + | 1.96404i | 0.260128 | + | 0.0697011i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.7583 | + | 7.16987i | −0.948424 | + | 0.254129i | ||||
\(797\) | −3.52193 | + | 13.1440i | −0.124753 | + | 0.465585i | −0.999831 | − | 0.0183975i | \(-0.994144\pi\) |
0.875078 | + | 0.483983i | \(0.160810\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.09808 | + | 26.4904i | −0.251112 | + | 0.937162i | ||||
\(800\) | −1.41421 | + | 1.41421i | −0.0500000 | + | 0.0500000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.7846 | + | 8.53590i | −0.522063 | + | 0.301413i | ||||
\(803\) | − | 15.6579i | − | 0.552555i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.58846 | − | 3.80385i | 0.232213 | − | 0.134068i | ||||
\(806\) | 2.17209 | + | 2.17209i | 0.0765085 | + | 0.0765085i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.56218 | − | 1.56218i | 0.0549572 | − | 0.0549572i | ||||
\(809\) | −6.69213 | + | 1.79315i | −0.235283 | + | 0.0630438i | −0.374534 | − | 0.927213i | \(-0.622197\pi\) |
0.139251 | + | 0.990257i | \(0.455531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.0000 | + | 25.9808i | −0.526721 | + | 0.912308i | 0.472794 | + | 0.881173i | \(0.343245\pi\) |
−0.999515 | + | 0.0311349i | \(0.990088\pi\) | |||||||
\(812\) | 10.6066 | + | 2.84203i | 0.372219 | + | 0.0997357i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.1244 | + | 8.66025i | −0.424958 | + | 0.303542i | ||||
\(815\) | 0.656339i | 0.0229905i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.73205 | − | 1.00000i | −0.0605968 | − | 0.0349856i | ||||
\(818\) | −14.1100 | + | 24.4392i | −0.493343 | + | 0.854495i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.09808 | − | 7.09808i | −0.247876 | − | 0.247876i | ||||
\(821\) | −44.6592 | − | 25.7840i | −1.55862 | − | 0.899868i | −0.997390 | − | 0.0722070i | \(-0.976996\pi\) |
−0.561228 | − | 0.827661i | \(-0.689671\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | − | 27.7128i | −0.557725 | − | 0.966008i | −0.997686 | − | 0.0679910i | \(-0.978341\pi\) |
0.439961 | − | 0.898017i | \(-0.354992\pi\) | |||||||
\(824\) | 5.27792i | 0.183865i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.80385 | + | 6.58846i | 0.132353 | + | 0.229242i | ||||
\(827\) | −10.7589 | − | 40.1528i | −0.374124 | − | 1.39625i | −0.854621 | − | 0.519253i | \(-0.826210\pi\) |
0.480497 | − | 0.876996i | \(-0.340456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.4186 | + | 12.4378i | 1.61218 | + | 0.431983i | 0.948692 | − | 0.316200i | \(-0.102407\pi\) |
0.663492 | + | 0.748184i | \(0.269074\pi\) | |||||||
\(830\) | 5.37945 | − | 3.10583i | 0.186724 | − | 0.107805i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.0980762 | − | 0.366025i | −0.00340018 | − | 0.0126896i | ||||
\(833\) | −9.02150 | − | 33.6687i | −0.312577 | − | 1.16655i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 37.3923 | − | 21.5885i | 1.29401 | − | 0.747099i | ||||
\(836\) | −12.4877 | − | 3.34607i | −0.431896 | − | 0.115726i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.24167 | − | 19.5622i | −0.181070 | − | 0.675764i | ||||
\(839\) | 12.9038 | + | 22.3500i | 0.445488 | + | 0.771608i | 0.998086 | − | 0.0618398i | \(-0.0196968\pi\) |
−0.552598 | + | 0.833448i | \(0.686363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.0000i | 1.58621i | ||||||||
\(842\) | −7.65806 | − | 13.2641i | −0.263914 | − | 0.457113i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.4186 | + | 8.90192i | 0.530730 | + | 0.306417i | ||||
\(845\) | 15.7458 | + | 15.7458i | 0.541673 | + | 0.541673i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.16987 | + | 5.49038i | −0.108918 | + | 0.188652i | ||||
\(848\) | 5.22715 | + | 3.01790i | 0.179501 | + | 0.103635i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 12.9282i | − | 0.443434i | ||||||
\(851\) | 20.9730 | − | 2.03339i | 0.718944 | − | 0.0697036i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.0358984 | + | 0.00961894i | 0.00122914 | + | 0.000329346i | 0.259434 | − | 0.965761i | \(-0.416464\pi\) |
−0.258204 | + | 0.966090i | \(0.583131\pi\) | |||||||
\(854\) | 7.02030 | − | 12.1595i | 0.240230 | − | 0.416090i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.5622 | − | 2.83013i | 0.361008 | − | 0.0967318i | ||||
\(857\) | −20.6448 | + | 20.6448i | −0.705213 | + | 0.705213i | −0.965525 | − | 0.260312i | \(-0.916175\pi\) |
0.260312 | + | 0.965525i | \(0.416175\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.0000 | − | 29.0000i | −0.989467 | − | 0.989467i | 0.0104779 | − | 0.999945i | \(-0.496665\pi\) |
−0.999945 | + | 0.0104779i | \(0.996665\pi\) | |||||||
\(860\) | −0.568406 | + | 0.328169i | −0.0193825 | + | 0.0111905i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 20.1962i | − | 0.687884i | ||||||
\(863\) | −8.18067 | + | 4.72311i | −0.278473 | + | 0.160777i | −0.632732 | − | 0.774371i | \(-0.718067\pi\) |
0.354259 | + | 0.935147i | \(0.384733\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.6865 | − | 19.6865i | 0.669362 | − | 0.669362i | ||||
\(866\) | −4.86679 | + | 18.1631i | −0.165380 | + | 0.617208i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.66025 | + | 9.92820i | −0.0902949 | + | 0.336985i | ||||
\(869\) | 8.24504 | − | 2.20925i | 0.279694 | − | 0.0749438i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.53590 | − | 0.411543i | −0.0520419 | − | 0.0139446i | ||||
\(872\) | 1.53433 | + | 2.65754i | 0.0519590 | + | 0.0899957i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.9282 | + | 12.9282i | 0.437303 | + | 0.437303i | ||||
\(875\) | −14.8492 | + | 3.97884i | −0.501996 | + | 0.134509i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.7321 | 1.88194 | 0.940969 | − | 0.338493i | \(-0.109917\pi\) | ||||
0.940969 | + | 0.338493i | \(0.109917\pi\) | |||||||
\(878\) | −29.5969 | −0.998849 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.00000 | + | 3.00000i | −0.101130 | + | 0.101130i | ||||
\(881\) | 10.0060 | − | 17.3309i | 0.337111 | − | 0.583893i | −0.646777 | − | 0.762679i | \(-0.723884\pi\) |
0.983888 | + | 0.178786i | \(0.0572169\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.53590 | − | 24.3923i | −0.219950 | − | 0.820866i | −0.984365 | − | 0.176141i | \(-0.943638\pi\) |
0.764414 | − | 0.644725i | \(-0.223028\pi\) | |||||||
\(884\) | 2.12132 | + | 1.22474i | 0.0713477 | + | 0.0411926i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.12436 | − | 22.8564i | 0.205752 | − | 0.767876i | ||||
\(887\) | −31.1870 | −1.04716 | −0.523579 | − | 0.851977i | \(-0.675403\pi\) | ||||
−0.523579 | + | 0.851977i | \(0.675403\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.03332 | −0.101734 | ||||||||
\(890\) | 1.91327 | − | 7.14042i | 0.0641329 | − | 0.239347i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.9282 | − | 9.19615i | −0.533316 | − | 0.307910i | ||||
\(893\) | 5.79555 | + | 21.6293i | 0.193941 | + | 0.723797i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.3923 | − | 33.5885i | 0.648213 | − | 1.12274i | ||||
\(896\) | 0.896575 | − | 0.896575i | 0.0299525 | − | 0.0299525i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.4641 | 0.516044 | ||||||||
\(899\) | −70.2030 | −2.34140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.6865 | + | 10.0981i | −1.25552 | + | 0.336416i | ||||
\(902\) | 10.0382 | + | 10.0382i | 0.334235 | + | 0.334235i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.92820 | − | 6.80385i | −0.130650 | − | 0.226293i | ||||
\(905\) | 28.7697 | + | 7.70882i | 0.956338 | + | 0.256250i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.56218 | − | 0.954483i | 0.118280 | − | 0.0316931i | −0.199193 | − | 0.979960i | \(-0.563832\pi\) |
0.317474 | + | 0.948267i | \(0.397166\pi\) | |||||||
\(908\) | −5.22715 | + | 19.5080i | −0.173469 | + | 0.647395i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.215390 | − | 0.803848i | 0.00714012 | − | 0.0266473i | ||||
\(911\) | −12.7279 | + | 12.7279i | −0.421695 | + | 0.421695i | −0.885787 | − | 0.464092i | \(-0.846381\pi\) |
0.464092 | + | 0.885787i | \(0.346381\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.60770 | + | 4.39230i | −0.251778 | + | 0.145364i | ||||
\(914\) | 0.693504i | 0.0229391i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.866025 | − | 0.500000i | 0.0286143 | − | 0.0165205i | ||||
\(917\) | 7.04386 | + | 7.04386i | 0.232609 | + | 0.232609i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.1244 | + | 11.1244i | −0.366959 | + | 0.366959i | −0.866367 | − | 0.499408i | \(-0.833551\pi\) |
0.499408 | + | 0.866367i | \(0.333551\pi\) | |||||||
\(920\) | 5.79555 | − | 1.55291i | 0.191074 | − | 0.0511981i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.73205 | − | 8.19615i | 0.155842 | − | 0.269926i | ||||
\(923\) | −0.896575 | − | 0.240237i | −0.0295111 | − | 0.00790749i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | − | 2.00000i | −0.394558 | − | 0.0657596i | ||||
\(926\) | − | 42.3992i | − | 1.39332i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.50000 | + | 4.33013i | 0.246200 | + | 0.142143i | ||||
\(929\) | −7.55652 | + | 13.0883i | −0.247921 | + | 0.429412i | −0.962949 | − | 0.269684i | \(-0.913081\pi\) |
0.715028 | + | 0.699096i | \(0.246414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.1244 | − | 20.1244i | −0.659549 | − | 0.659549i | ||||
\(932\) | −8.12493 | − | 4.69093i | −0.266141 | − | 0.153656i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.66025 | + | 4.60770i | 0.0870462 | + | 0.150768i | ||||
\(935\) | − | 27.4249i | − | 0.896889i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.59808 | + | 13.1603i | 0.248218 | + | 0.429927i | 0.963032 | − | 0.269389i | \(-0.0868216\pi\) |
−0.714813 | + | 0.699315i | \(0.753488\pi\) | |||||||
\(938\) | −1.37705 | − | 5.13922i | −0.0449622 | − | 0.167801i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.09808 | + | 1.90192i | 0.231514 | + | 0.0620339i | ||||
\(941\) | 13.1998 | − | 7.62089i | 0.430300 | − | 0.248434i | −0.269174 | − | 0.963091i | \(-0.586751\pi\) |
0.699475 | + | 0.714658i | \(0.253417\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.19615 | − | 19.3923i | −0.169210 | − | 0.631500i | ||||
\(944\) | 1.55291 | + | 5.79555i | 0.0505431 | + | 0.188629i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.803848 | − | 0.464102i | 0.0261353 | − | 0.0150892i | ||||
\(947\) | −27.6651 | − | 7.41284i | −0.898995 | − | 0.240885i | −0.220410 | − | 0.975407i | \(-0.570740\pi\) |
−0.678585 | + | 0.734522i | \(0.737406\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.626933 | + | 2.33975i | 0.0203511 | + | 0.0759514i | ||||
\(950\) | −5.27792 | − | 9.14162i | −0.171238 | − | 0.296593i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.19615i | 0.265639i | ||||||||
\(953\) | 7.26054 | + | 12.5756i | 0.235192 | + | 0.407364i | 0.959328 | − | 0.282292i | \(-0.0910948\pi\) |
−0.724137 | + | 0.689657i | \(0.757761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.3923 | − | 11.1962i | −0.627520 | − | 0.362299i | ||||
\(956\) | −16.7303 | − | 16.7303i | −0.541097 | − | 0.541097i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.39230 | + | 2.41154i | −0.0449833 | + | 0.0779134i | ||||
\(959\) | −17.6505 | − | 10.1905i | −0.569963 | − | 0.329068i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 34.7128i | − | 1.11977i | ||||||
\(962\) | 1.46498 | − | 1.77955i | 0.0472329 | − | 0.0573749i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.2942 | + | 3.56218i | 0.428178 | + | 0.114730i | ||||
\(965\) | −3.55412 | + | 6.15591i | −0.114411 | + | 0.198166i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.2679 | + | 3.28719i | −0.394511 | + | 0.105709i | −0.450620 | − | 0.892716i | \(-0.648797\pi\) |
0.0561095 | + | 0.998425i | \(0.482130\pi\) | |||||||
\(968\) | −3.53553 | + | 3.53553i | −0.113636 | + | 0.113636i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.633975 | + | 0.633975i | 0.0203557 | + | 0.0203557i | ||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 0.497423i | − | 0.0159466i | ||||||
\(974\) | 11.3509 | − | 6.55343i | 0.363705 | − | 0.209985i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.83013 | − | 7.83013i | 0.250636 | − | 0.250636i | ||||
\(977\) | 13.5601 | − | 50.6071i | 0.433827 | − | 1.61906i | −0.310031 | − | 0.950726i | \(-0.600340\pi\) |
0.743858 | − | 0.668338i | \(-0.232994\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.70577 | + | 10.0981i | −0.0864768 | + | 0.322736i | ||||
\(980\) | −9.02150 | + | 2.41730i | −0.288181 | + | 0.0772179i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.7583 | + | 5.83013i | 0.694336 | + | 0.186047i | ||||
\(983\) | 12.1595 | + | 21.0609i | 0.387828 | + | 0.671738i | 0.992157 | − | 0.124997i | \(-0.0398920\pi\) |
−0.604329 | + | 0.796735i | \(0.706559\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.6865 | + | 13.6865i | 0.436089 | + | 0.436089i | ||||
\(986\) | −54.0733 | + | 14.4889i | −1.72204 | + | 0.461420i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.00000 | 0.0636285 | ||||||||
\(989\) | −1.31268 | −0.0417407 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.6603 | − | 34.6603i | 1.10102 | − | 1.10102i | 0.106731 | − | 0.994288i | \(-0.465962\pi\) |
0.994288 | − | 0.106731i | \(-0.0340385\pi\) | |||||||
\(992\) | −4.05317 | + | 7.02030i | −0.128688 | + | 0.222895i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.803848 | − | 3.00000i | −0.0254965 | − | 0.0951542i | ||||
\(995\) | −41.5534 | − | 23.9909i | −1.31733 | − | 0.760561i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.04552 | − | 30.0263i | 0.254804 | − | 0.950942i | −0.713395 | − | 0.700762i | \(-0.752844\pi\) |
0.968199 | − | 0.250180i | \(-0.0804898\pi\) | |||||||
\(998\) | −1.41421 | −0.0447661 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 666.2.be.c.341.1 | yes | 8 | |
3.2 | odd | 2 | inner | 666.2.be.c.341.2 | yes | 8 | |
37.14 | odd | 12 | inner | 666.2.be.c.125.2 | yes | 8 | |
111.14 | even | 12 | inner | 666.2.be.c.125.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
666.2.be.c.125.1 | ✓ | 8 | 111.14 | even | 12 | inner | |
666.2.be.c.125.2 | yes | 8 | 37.14 | odd | 12 | inner | |
666.2.be.c.341.1 | yes | 8 | 1.1 | even | 1 | trivial | |
666.2.be.c.341.2 | yes | 8 | 3.2 | odd | 2 | inner |